Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry

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A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (B1) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to O. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to I.

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Rosa, Massimiliano; Warsa, James S & Kelley, Timothy M January 1, 2009.

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A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (B1) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to O. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to I.

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  • M&C 2009 ; May 3, 2009 ; Saratoga Springs, NY

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  • Report No.: LA-UR-09-00658
  • Report No.: LA-UR-09-658
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956371
  • Archival Resource Key: ark:/67531/metadc927666

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  • January 1, 2009

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 3:56 p.m.

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Rosa, Massimiliano; Warsa, James S & Kelley, Timothy M. Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc927666/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.